A perturbation expansion has been performed for the critical lines of the eight-vertex and Ashkin-Teller models around the decoupling point. The critical temperature and the details of the mapping of these lines onto the Gaussian-model critical line is calculated to second order in the marginal parameters. We find agreement with the exactly known results for these models and with the mapping formalism of Kadanoff and Brown.

• Received 27 May 1980

DOI:https://doi.org/10.1103/PhysRevB.23.1459